Fourier transformation can improve quadrature efficiency of Laplace distribution
by Jinhyo Kim and Sangwon Seo
.
Abstract:
A numerical quadrature of a particular probability integral is concerned
with using the Fourier transformation which smoothes the stiffness. \ The Fourier
transformation of the Laplace distribution becomes, in a statistical sense, the
Cauchy distribution. \ It is shown that the Gauss-Hermite quadrature of the Cauchy
distribution, equivalent to the {\em Fourier-transformed} Laplace distribution, exhibits
{\em better numerical} efficiency than the Gauss-Hermite quadrature of the {\em
untransformed} Laplace distribution. \ A numerical example supports the analytic argument.
Key Words:
Fourier transformation, Gauss-Hermite quadrature,
Laplace distribution, Cauchy distribution
Authors:
Jinhyo Kim
,
jinkim@stats.snu.ac.kr
Sangwon Seo,
sangwon@math.snu.ac.kr
Editor:
John P. Hinde
,
J.P.Hinde@exeter.ac.uk
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